Solving for a side in a right triangle Quiz 1

Question 1

In the given figure, find the length of the hypotenuse. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/f9db1933-f3df-4f0f-9808-4344f00897688822096487274415686.png"/>

Accepted Answer

$$14cm$$

Answer

$$10\sqrt{2}cm$$

Answer

$$12\sqrt{3}cm$$

Answer

$$15cm$$

Question 2

If the hypotenuse of a right-angled triangle is $$4\sqrt{29}cm$$ and the perpendicular is $$12cm$$ more than its base, then find the length of the base.

Accepted Answer

$$8cm$$

Answer

$$6cm$$

Answer

$$10cm$$

Answer

$$11cm$$

Question 3

In the given figure if the sum of the two sides RS and ST is given by $$6a+150$$, then at what height is the parachute flying from the ground level? <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/0de197e0-ea38-40ef-b9d1-577b91628c121477255322890109773.png"/>

Accepted Answer

$$250\sqrt{3}	ext{ units}$$

Answer

$$150\sqrt{3}	ext{ units}$$

Answer

$$200\sqrt{3}	ext{ units}$$

Answer

$$500\sqrt{3}	ext{ units}$$

Question 4

If $$x,y	ext{ and }z$$ are the lengths of the three sides $$RS,ST	ext{ and }RT$$ respectively of a right $$\Delta RST$$ at $$\angle T=90{}^\circ $$ such that $$x:y:z=2:5:6$$ and $$\cos R=\dfrac{x}{32}$$, then find the value of $$z$$.

Accepted Answer

60 units

Answer

30 units

Answer

42 units

Answer

54 units

Question 5

$$XD$$ is the altitude of an isosceles $$\Delta XYZ$$ such that $$XY=XZ$$. If $$a+b=7,XY=3a+2,YD=b+1	ext{ and }XZ=b+3$$, then find the length of $$XD$$ in $$cm$$.

Accepted Answer

$$6\sqrt{3}cm$$

Answer

$$4\sqrt{3}cm$$

Answer

$$7\sqrt{5}cm$$

Answer

$$7\sqrt{2}cm$$